ANN’s single output representing value
Yes, this is possible. The only restriction on the range of output values is due to the activation function, if there is one. If, for example, the activation function is a sigmoid, the output would be restricted to values between 0 and 1. You can of course choose an activation function best suited to your problem, even if that means having none. 

In your case, if you really want the output of your network to be between 50 and 250, you could use a scaled and shifted sigmoid as your activation: 200*sig(w*x+b)+50. 

But, as was pointed out in comments below, having a single output neuron may not be the best architecture for this problem.